Problem: Rewrite as a simplified fraction. ${1.\overline{76} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 176.7676...\\ 1x &= 1.7676...\end{align*}}$ Subtracting the two equations, we have: ${99x = 175}$ ${x = \dfrac{175}{99}} \text{or} {1 \dfrac{76}{99}}$